Chapter 2Chapter ObjectivesSlide 3Statistical TermsNumbersNumber ScalesNominal Scale: This scale refers to a classificatory approach, i.e., categorizing observations. Distinct characteristics must exist to categorize: gender, race essentially you can only be assigned one group. KEY: to distinguish one from another.Ordinal Scale: This scale puts order into categories. It only ranks categories by ability, but there is no specific quantification between categories. It is only placement, e.g., judging a swimming race without a stopwatch, i.e., there is no quantitiy to determine the difference between ranks. KEY: placement without quantification.Interval Scale: This scale adds equal intervals between observed categories. We know that 75 points is halfway between scores of 70 and 80 points on a scale. KEY: how much was the difference between 1st and 2nd place?Ratio Scale: this scale has all the qualities of an interval scale with the added property of a true zero. Not all qualities can be assigned to a ratio scale. KEY: quality of measurement must represent a true zero.Normal DistributionCharacteristics of Normal CurveSlide 13Different CurvesScore RankSlide 16Measures of Central TendencyMeanSymbols Used to Calculate MeanMedianSteps in Calculation of MedianModeWhich Measure of Central Tendency is Best for Interpretation of Test Results?Measures of VariabilityRangeQuartile DeviationSlide 27Steps for Calculation of Q3QuartilesSlide 30Standard DeviationCharacteristics of Standard DeviationSlide 33Calculation of Standard Deviation with X2Calculation of Standard Deviation with d2Interpretation of Standard Deviation in Tables 2.3 and 2.4Relationship of Standard Deviation and Normal CurveSlide 3860-sec Sit-up Test to Two Fitness ClassesCalculation of Percentile Rank through Use of Mean and Standard Deviation.Which Measure of Variability is Best for Interpretation of Test Results?Percentiles and Percentile RanksWeakness of PercentilesAnalysis of Grouped DataTennis Serve Test ScoresSteps to Construct Frequency DistributionSlide 47Slide 48Slide 49Slide 50Slide 51Slide 52The ModeThe MeanSlide 55Slide 56The MedianSlide 58Slide 59Slide 60The Quartile DeviationSlide 62The Standard DeviationSlide 64GraphsStandard Scoresz-ScoresSlide 68T-ScoresSlide 70Slide 71Slide 72Slide 73Slide 74Percentiles© 2006 McGraw-Hill Higher Education. All rights reserved.Chapter 2Describing and Presenting a Distribution of Scores© 2006 McGraw-Hill Higher Education. All rights reserved.Chapter 2© 2006 McGraw-Hill Higher Education. All rights reserved.Chapter ObjectivesAfter completing this chapter, you should be able to1. Define all statistical terms that are presented.2. Describe the four scales of measurement and provide examples of each.3. Describe a normal distribution and four curves for distributions that are not normal.4. Define the terms measures of central tendency and measures of variability.5. Define the three measures of central tendency, identify the symbols used to represent them, describe their characteristics, calculate them with ungrouped and grouped data, and state how they can be used to interpret data.© 2006 McGraw-Hill Higher Education. All rights reserved.Chapter Objectives6. Define the three measures of variability, identify the symbols used to represent them, describe their characteristics, calculate them with ungrouped and grouped data, and state how they can be used to interpret data.7. Define percentile and percentile rank, identify the symbols used to represent them, calculate them with ungrouped and grouped date, and state how they can be used to interpret data.8. Define standard scores, calculate z-scores, and interpret their meanings.© 2006 McGraw-Hill Higher Education. All rights reserved.Statistical Terms•data•variable•population•sample•random sample•parameter•Statistic•descriptive statistics•inferential statistics•discrete data•continuous data•ungrouped data•grouped data© 2006 McGraw-Hill Higher Education. All rights reserved.Numbers•Numbers mean different things in different situations. Consider three answers that appear to be identical but are not.•“What number were you wearing in the race?” “5”•What place did you finish in ?” “5”•How many minutes did it take you to finish?” “5”© 2006 McGraw-Hill Higher Education. All rights reserved.Number Scales•Nominal Scale•Ordinal Scale•Interval•Ratio© 2006 McGraw-Hill Higher Education. All rights reserved.Nominal Scale: This scale refers to a classificatory approach, i.e., categorizing observations. Distinct characteristics must exist to categorize: gender, race essentially you can only be assigned one group. KEY: to distinguish one from another.© 2006 McGraw-Hill Higher Education. All rights reserved.Ordinal Scale: This scale puts order into categories. It only ranks categories by ability, but there is no specific quantification between categories. It is only placement, e.g., judging a swimming race without a stopwatch, i.e., there is no quantitiy to determine the difference between ranks. KEY: placement without quantification.© 2006 McGraw-Hill Higher Education. All rights reserved.Interval Scale: This scale adds equal intervals between observed categories. We know that 75 points is halfway between scores of 70 and 80 points on a scale. KEY: how much was the difference between 1st and 2nd place?© 2006 McGraw-Hill Higher Education. All rights reserved.Ratio Scale: this scale has all the qualities of an interval scale with the added property of a true zero. Not all qualities can be assigned to a ratio scale. KEY: quality of measurement must represent a true zero.© 2006 McGraw-Hill Higher Education. All rights reserved.Normal Distribution•Most statistical methods are based on assumption that a distribution of scores is normal and that the distribution can be graphically represented by the normal curve (bell-shaped).•Normal distribution is theoretical and is based on the assumption that the distribution contains an infinite number of scores.© 2006 McGraw-Hill Higher Education. All rights reserved.Characteristics of Normal Curve•Bell-shaped curve•Symmetrical distribution about vertical axis of curve•Greatest number of scores found in middle of curve•All measures of central tendency at vertical axis© 2006 McGraw-Hill Higher Education. All rights reserved.meanmedianmode© 2006 McGraw-Hill Higher Education. All rights reserved.Different Curves•leptokurtic -